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Parameter Estimation in Mathematical Models for Spectroscopic Observations

Radmila Pribic
Journal / Anthology

Ph.D. thesis, Vrije Universiteit
Year: 1996

Advanced tools for parameter estimation in mathematical models are available in applied mathematics and statistics, but not well integrated in spectroscopy. We realized this integration in an open problem solving environment (PSE), which focuses upon the iterative refining of mathematical models for spectroscopic observations. The solution of a spectroscopic problem is structured systematically by the three steps in each cycle of the modelling process: building a model, parameter estimation and interpretation of the model usefulness. It is shown that this structure is sufficiently flexible and enables guidance to the user in the process of refining of models. Two real-world problems (1) prediction of protein secondary structure from steady state spectra, and (2) estimation of decay lifetimes of photosynthetic reactions from time resolved spectra, were solved within this PSE, demonstating the completeness of the modelling tools and the guidance to an experimenter. The problem of prediction from spectra was better understood by recognizing it as a calibration, and by the introduction of a statistical test. Because of its support for symbolics, numerics and graphic, Mathematica was chosen as programming environment for the PSE. A major advantage of the symbolics is that model changes propagate through the PSE and thus require minimal programming effort. This contributes significantly to the openness of the environment created. The price that has to be paid for this is in performance requirements of the hardware: only state-of-the-art systems can be used.

*Mathematics > Probability and Statistics